Is it 1994? Two people, two Windows logins.
You have two users using a computer, why are you making things difficult for yourself instead of going down the obvious route of having two user accounts?
Not sure if I follow that sorry. Can you explain it again?If you really want to do the user switching in a browser instead of the OS then delegate account access to the other account, and then log in using the account with the delegated access and you will be able to switch between the two mailboxes using the Google account picker thing at the top right.
For example, here's something that's instantly easier:- https://accounts.google.com/AccountChooser?service=mail
Afaik that account switcher wants passwords re-entering, at least it does for me.
Like that. Will bookmark for my parents.
Alternatively create two user profiles in Firefox and use a different shortcut to access each one http://kb.mozillazine.org/Command_line_arguments#List_of_command_line_arguments_.28incomplete.29